We propose a \(\mathsf {CAE}\)  learning system, as depicted in Fig. REF , where the
input data are the \({N}\)  subcarries \(\lbrace {X}_k\rbrace _{k=0}^{{N}-1}\)  in the frequency domain. Then the signal is zero-padded and converted to the time domain by \(\mathsf {FFT}\) , outputting \(\lbrace {x}_n\rbrace _{n=0}^{{{LN}-1}}\) .
These symbols serve as input to the encoder, which acts as a \(\mathsf {PAPR}\)  reduction block, followed by a filter for optimizing the spectral behavior.
Both the encoder and the decoder are composed of two convolutional layers, each followed by a non-linear activation function and batch normalization [1]}, and then a fully connected layer.
We have tested several activation functions, including sigmoid, rectified linear unit (\(\mathsf {RELU}\) ), Gaussian error linear unit (\(\mathsf {GELU}\) ), and scaled exponential linear unit (\(\mathsf {SELU}\) ) [2]}. Empirically, \(\mathsf {SELU}\)  activation provides the best results for our \(\mathsf {CAE}\)  scheme.
In addition, the encoder has a power normalization layer [3]}, which
insures that the transmitted signal meets the power constraints.
